Percolation-Based Techniques for Upscaling the Hydraulic Conductivity of Semi-Realistic Geological Media

I tested three schemes for upscaling the hydraulic conductivity (K) on aquifers with bimodal K distributions. This bimodality (e.g., sand and mud deposits) was intended to capture typical geological conditions. Results were tested with a numerical model. Upscaling techniques used were inspired by schemes interpolating between arithmetic and harmonic means, but are based on percolation theory: 1) Critical path analysis (CPA), 2) Percolation path analysis (PPA, or standard scaling), and a novel scaling approach. Models chosen were both spatially correlated and uncorrelated, with important differences in critical percolation probabilities, Pc. Volume fractions Ps and 1-Ps (with Ps = sand volume fraction) were assigned to each mode of the distribution of K. I found that application of the requirement for CPA to interpolate smoothly between the parallel and series configurations makes it satisfactory only for Ps\u3ePc. PPA generally underestimates K. The novel scaling technique has the widest generality